Hybrid Local Polynomial Wavelet Shrinkage for Stationary Correlated Data

Local Polynomial Wavelet Shrinkage estimator (LPWS) is an attractive technique used to cope with the boundary problem present in wavelet shrinkage. However, this combined estimator seems to be quite sensitive to the presence of correlated noise. In this paper, the practical consequences of this sensitivity are explained; including the breakdown of several popular thresholding selection methods. The term-by term level dependent thresholding has been investigated as an effective solution for recovering a signal contaminated with correlated noise. A simulation study is conducted to evaluate both EbayesThresh and level dependent cross validation under a variety of test function, noise structure, signal to noise ratio and sample size. Results showed that thresholding by level dependent cross validation is preferable.